You can open and add messages to tickets via the API, but apparently it is not possible to close them. When I try to send a PUT to /api/v1/tickets/ticket_id.json and set 'state' to 'closed' I get the following error:

{'errors': {'message': 'Admin required: Not signed or not admin. No token; Unverified; Signature verification failed; User not signed: oauthenticate failed', 'type': 'unauthorized'}}